Basic thought of Sampling The data is very important in every field for decision making whether it is medical sciences, engineering sciences, agricultural sciences and management sciences etc. for this we need to plan the correct data. If we don’t have correct data then based on that we cannot plan good decisions and it will provide misleading results. So, to achieve or plan the right data it is necessary to have the right technique which is to be used while collecting data and an appropriate method of data collection is preferred. From this, the two important questions arise (i) what are those methods required to obtain paramount data or sample and (ii) how best to use the data or sample to estimate the characteristic of the whole population i.e., what are those methods by which we can study our population parameters to draw a proper statistical inference.

Sample Design Sample design is a specific system for obtaining a sample from a given population. For the effective planning and sample survey, this sample design is the framework or road map that serves as the basis for the selection of the survey sample and affects many other important aspects of a survey as well. It is a definite plan for obtaining a sample from a given population. Sampling design refers to the procedure that the researcher would adopt in selecting items as the sample. Also, sampling design is a working plan that specifies the sample frame, sample size, sample selection and estimation method in detail. The blueprint for obtaining a sample from the sampling frame and this technique used in drawing a sample is known as sample design or sampling design. This whole process is done before the determination of data collection.

Simple Random Sampling (SRS) Simple random sampling is probability sampling and refers to a technique of sampling where each and every unit of the population have an equal and independent opportunity of being selected and included in the sample during the sampling. In the SRS the selection of the sample depends on the chance factor and is also known as the method of probability sampling. There are two ways in which SRS can be performed: SRSWR: Simple Random Sampling With Replacement SRSWOR: Simple Random Sampling Without Replacement

Stratified Sampling (Meaning and Concept) The word ‘stratify’ comes from the Latin word, meaning ‘to make layers’, thus in stratified sampling the whole population is considered to be classified into some mutually exclusive layers or subgroups or classes also called strata. The strata do not overlap and they constitute the whole population. Why the population is considered to be divided into different strata (or layers or subgroups or classes)?

Systematic Sampling (Meaning and Concept) In this chapter, we are going to discuss the systematic random sampling technique. This is a random / probability / quantitative sampling method. In our previous chapter, we discussed the stratified random sampling technique. We have said that this technique is used when the population is heterogeneous and needs to be stratified into homogeneous groups. We have also discussed steps to be followed when using stratified random sampling as well as the strengths and limitations of stratified random sampling. Systematic sampling is a commonly employed technique if a complete and up-to-date list of the sampling units is available. The procedure involves choosing the very first object arbitrarily and the remaining members of the sample will be selected naturally according to any pre-decided sequence containing regular spacing of units. In this method, units of the population are numerically, geographically, and alphabetically arranged either in ascending or descending order (generally ascending order is preferred). When the ordering of the elements is related to the characteristic of interest,

Cluster Sampling (Meaning and Concept) Cluster sampling is a special type of sampling which is used when we have to make a large survey such as a survey for the whole country and whole state etc. to know the privilege. Under this method, the total population is divided into some recognizable subdivisions known as clusters. Out of all the clusters, a given number of clusters are chosen at random. All the items covered by the selected clusters are included in the sample. A sampling technique in which we divide the whole population into groups or subgroups in such a way that there is heterogeneity within each group and homogeneity among the groups and then a simple random sample of n groups is selected from a total of N groups of population and finally all the units of selected clusters from our sample.

Multistage Sampling Multistage sampling is a form of random sampling where samples are selected in a sequence of stages. Where each sample is drawn from the exclusive previously selected samples. This sampling is not done once but at multiple stages. It differs from cluster sampling in the sense that cluster uses all the subjects within a cluster whereas multistage selects a sample from within the selected group. Groups are randomly chosen from a population; subgroups from these groups are randomly chosen and then randomly chosen to be surveyed. This is an extension of cluster sampling, which is carried out in multiple stages say two, three or four stages. In the first stage, the universe is divided into some clusters from which certain clusters are selected at random at the first stage samples. In the second stage, the selected first stage samples are again subdivided into some clusters from which again certain clusters are selected at random as the second stage samples. In the third stage, the selected second stage samples are again subdivided into some clusters from which certain clusters are again selected at random as the third stage samples.

Non-Probability sampling methods are also known as non-random sampling methods or deliberate sampling. These types of methods are reliant on the researcher’s ability to select members at random. These sampling methods are not fixed or pre-defined selection processes making it difficult for all elements of the population to have equal opportunities to be included in the sample. Types of non-probability sampling techniques 1. Judgmental or Purposive sampling This technique involves the purposive selection of units of samples based on the judgement of the researcher. The researcher selects the sample on the basis of his a priori knowledge and experience.

Yet now we have discussed probability sampling techniques in which sampling units are assigned with equal probabilities. But sometimes in practice if want to draw a sample with unequal probabilities i.e., every sampling unit is assigned with varying probabilities and we draw a sample from these units with the help of equal probability methods, then the results are not as much efficient as compared to unequal probability sampling. Simple random sampling is a procedure wherein the chance of selection of every unit in the required sample is equal. However, the use of simple random sampling is not advisable when the units differ substantially in size as the significance of unit size is ignored. The basic idea of this type of probability technique is that chance of each unit of a population being selected in the sampling is proportional to its size. The units vary significantly in size and the variable under study is largely related to the size of the unit. Therefore, the probabilities fixed for each unit are proportional to their sizes.

Introduction In some practical field situations, the results are described by some percentages or proportions. In agricultural field conditions, if any disease prevalence is to find then in the form of percentage or proportion, we can say how much disease rate is present i.e., 10 % or may be any other. So, in those situations, we need to describe our results in proportions. Similarly, in many fields such as medical sciences, social sciences and other allied sciences this type of results in proportions we need to describe.

In our previous chapters, we have discussed various sampling designs or techniques such as simple random sampling, stratified sampling, systematic sampling and cluster sampling recently we have discussed unequal probability sampling i.e., probability proportional to size sampling. In all these sampling designs the variable of interest (generally there is only one variable of interest) which we have considered and perform our estimation based on that single variable. There are some other variables which are related to our variable of interest and if we utilize those variables, we may gain some efficiency in our estimator i.e., if we take some correlated variables with our variable of interest or study variable by this, we can enhance our estimation. The variable which is correlated with the study variable is usually known auxiliary variable or supporting variable or supplementary variable or benchmark variable. This auxiliary variable is utilized in two stages either in the design stage or estimation stage. Graunt (1662) was the first who used auxiliary information to estimate the population size of England. After this Laplace used auxiliary information for the estimation of the population in France.

Non-Response Non response occurs when respondents are not available or do not occur in the survey and refuse to respond by any means. This non response is mainly of two types either item non response or unit non response. If we are conducting an online survey and mailing a questionnaire to various persons. But sometimes we get a reply for some questions and sometimes not i.e., in case of questions in which income is concerned. In some cases, the mail is ignored due to lack of time. So, if the whole questionnaire is ignored by any means, then it is known as non-response and if some of the questions are ignored due to their fussy nature such type of response is known as a unit non response. Such types of non-response problems are very common in surveys. Whenever we carry out a survey non response always exists because it is almost impossible to get every response from each individual. The individual chosen for the sample is not ready to participate in the survey is known as non-response. This type of selection bias is unit/item non response.

Suggested Readings and References